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Total Positivity, Flag Varieties And Quantum Cohomology

In: European Women In Mathematics

Author

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  • KONSTANZE RIETSCH

    (Department of Mathematics, King's College, University of London, UK)

Abstract

The aim of this contribution is to give an introduction to some aspects of quantum cohomology rings of flag varieties especially explaining their relationship with total positivity. The results outlined here are written up in greater generality elsewhere1. In this paper we give a simplified exposition focusing on the variety of complete flags. We explain how the quantum cohomology ring for the full flag variety can be used to study totally positive uni-triangular Toeplitz matrices. The special case considered here contains most of the main ideas but avoids some of the technical difficulties which come up in the more general setting of partial flag varieties and total nonnegativity.

Suggested Citation

  • Konstanze Rietsch, 2003. "Total Positivity, Flag Varieties And Quantum Cohomology," World Scientific Book Chapters, in: Emilia Mezzetti & Sylvie Paycha (ed.), European Women In Mathematics, chapter 8, pages 149-167, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812704276_0008
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